Underwater acoustic instruments can be deployed in oceans or other bodies of water and can be configured to receive signals from an acoustic source. Examples of underwater acoustic instruments can include hydrophone modules, ocean bottom seismometers, current profilers, or various autonomous underwater vehicles such as, for example, seagliders. Alternatively, acoustic instruments can be parts of more complex systems such as naval submarines, research submersibles, etc. These instruments are designed to take measurements of underwater pressure waves transmitted by various sources. All collected data samples should be accurately associated with time stamps at which the data were collected for correct interpretation and post-processing. The knowledge of accurate time stamps for the collected data can be important in a variety of contexts. Such contexts could include surveillance, communications, remote sensing, and petroleum exploration, as examples. Being able to accurately determine the precise time and location the data were acquired can be important to ensuring that the data are interpreted accurately.
Clock drift can lead to errors in interpreting the data received by an underwater instrument. For instance, in sonar applications, clock drift can lead to errors in estimating the range or bearing of a target. In the context of petroleum exploration, images of the subsurface structure, including oil- and gas-bearing formations, are improved with better timing and location information. In the context of communications applications, the synchronization of the received waveform could be inaccurate leading to errors in interpreting the received data (i.e., resulting in increased bit error rates).
Conventionally, models of clock drift can be employed to correct for errors associated with clock drift. Various models of clock drift, for example, models that assume that the frequency of the clock is offset by a constant value or drifts linearly over time, could be used to correct the received data for errors associated with clock drift. However, the accuracy of the models can be questionable and can still cause errors in interpreting the data received by an underwater instrument. Also, generally clocks do not drift monotonically. They can speed-up or slow-down in an arbitrary and unpredictable fashion throughout the deployment.
Thus, a more accurate method of estimating clock drift of an underwater instrument is desirable in order to further increase the fidelity of the data collection and minimize any errors caused by clock drift.